Inventory management system in a print-production environment

ABSTRACT

An inventory management system for forecasting demand in a print production environment may include a computing device and a computer-readable storage medium in communication with the computing device. The computer-readable storage medium may include programming instructions for updating a predictive model with intervention information comprising an anticipated demand value and a confidence value associated with the anticipated demand value. The predictive model may be associated with a demand distribution of a print-related service. The computer-readable storage medium may include programming instructions for generating a demand forecast associated with the print-related service by using the updated predictive model, using the generated demand forecast to compare a current inventory level associated with the print-related service to an anticipated inventory level associated with the demand forecast of the print-related service, and ordering additional inventory in response to the current inventory level being less than the anticipated inventory level.

BACKGROUND

Inventory management systems in production environments requiresufficient inventory to satisfy demand. To avoid stockouts and to reducecosts associated with holding inventory, it is common for inventorymanagement systems to predict inventory levels by forecasting demandfrom historical demand data. However, this type of forecasting is oftenchallenging for inventory with scant historical data. For example, someinventory may only have quarterly inventory information going back oneyear. Models of such inventory information typically yield inaccurateresults, and fitting models of such information by hand is timeconsuming and cumbersome.

SUMMARY

Before the present methods are described, it is to be understood thatthis invention is not limited to the particular systems, methodologiesor protocols described, as these may vary. It is also to be understoodthat the terminology used herein is for the purpose of describingparticular embodiments only, and is not intended to limit the scope ofthe present disclosure which will be limited only by the appendedclaims.

It must be noted that as used herein and in the appended claims, thesingular forms “a,” “an,” and “the” include plural reference unless thecontext clearly dictates otherwise. Unless defined otherwise, alltechnical and scientific terms used herein have the same meanings ascommonly understood by one of ordinary skill in the art. As used herein,the term “comprising” means “including, but not limited to.”

In an embodiment, an inventory management system for forecasting demandin a print production environment may include a computing device and acomputer-readable storage medium in communication with the computingdevice. The computer-readable storage medium may include one or moreprogramming instructions for updating a predictive model withintervention information comprising an anticipated demand value and aconfidence value associated with the anticipated demand value. Thepredictive model may be associated with a demand distribution of aprint-related service in a print production environment. Thecomputer-readable storage medium may include one or more programminginstructions for generating a demand forecast associated with theprint-related service by using the updated predictive model, using thegenerated demand forecast to compare a current inventory levelassociated with the print-related service to an anticipated inventorylevel associated with the demand forecast of the print-related service,and ordering additional inventory in response to the current inventorylevel being less than the anticipated inventory level.

In an embodiment, a method of forecasting demand in a print productionenvironment may include updating a predictive model with interventioninformation including an anticipated demand value and a confidence valueassociated with the anticipated demand value. The predictive model maybe associated with a demand distribution of a print-related service in aprint production environment. The method may include generating a demandforecast associated with the print-related service by using the updatedpredictive model, using the generated demand forecast to compare acurrent inventory level associated with the print-related service to ananticipated inventory level associated with the demand forecast of theprint-related service and ordering additional inventory in response tothe current inventory level being less than the anticipated inventorylevel.

BRIEF DESCRIPTION OF THE DRAWINGS

Aspects, features, benefits and advantages of the present invention willbe apparent with regard to the following description and accompanyingdrawings, of which:

FIG. 1 illustrates an exemplary method of forecasting demand in a printproduction environment according to an embodiment.

FIG. 2 illustrates exemplary time series according to an embodiment.

FIG. 3 depicts a block diagram of exemplary internal hardware that maybe used to contain or implement program instructions according to anembodiment.

DETAILED DESCRIPTION

For purposes of the discussion below, a “print production environment”refers to an entity that includes a plurality of print productionresources. A print production environment may be a freestanding entity,including one or more print-related devices, or it may be part of acorporation or other entity. Additionally, a print productionenvironment may communicate with one or more servers by way of a localarea network or a wide area network, such as the Internet, the WorldWide Web or the like.

A “print production resource” refers to a device capable of performingone or more print-related services. A print production resource mayinclude a printer, a cutter, a collator or the like.

A “job” refers to a logical unit of work that is to be completed for acustomer. A job may include one or more print jobs from one or moreclients. A print production environment may include a plurality of jobs.

A “print job” refers to a job processed in a print productionenvironment. For example, a print job may include producing credit cardstatements corresponding to a certain credit card company, producingbank statements corresponding to a certain bank, printing a document, orthe like.

A “print-related service” refers to a service performed by one or moreprint production resources. For example, copying, scanning, collatingand binding are exemplary print-related services.

FIG. 1 illustrates an exemplary method of forecasting demand in a printproduction environment according to an embodiment. As illustrated byFIG. 1, a predictive model may be identified 100. In an embodiment, apredictive model may be a mathematical or statistical model forforecasting time series data. For example, a Bayesian model may be apredictive model.

In an embodiment, the identified model may be associated with a demanddistribution of a print-related service in the print productionenvironment. In an embodiment, a demand distribution may refer to demandfor the print-related service over a period of time. For example, amodel may correspond to a binding print-related service in a printproduction environment. The model may be associated with a demanddistribution corresponding to binding, and the demand distribution mayrepresent the number of print jobs requiring binding over a certain timeperiod.

In an embodiment, the difficulties associated with forecasting demand ina print production environment may be ameliorated by the incorporationof historical data, subjective estimates of likely demand behavior, anability to modify forecasted values, an assignment of uncertainty valuesto the forecasts to estimate the probability of satisfying service levelagreements and/or the like.

In an embodiment, product demand may be represented as a series ofvalues. Product demand may be the demand associated with printproduction inventory such as supplies for creating print jobs, finishedprint jobs and/or the like. In an embodiment, the series of values mayinclude variation, and may be represented as a time series, randomprocess and/or the like. An inventory system may use the observations ofa time series of historical demand to predict or forecast future demandso that sufficient inventory may be available to satisfy the futuredemand.

For example, a First Order Dynamic Linear Model may have an observationpart and a system part. Each part may represent a source of uncertaintyabout future values. In an embodiment, new observations may be used toupdate the system part of the model. Updating the model may allow it totrack changing demand distributions which may be helpful in forecastingpotentially erratic behavior of a print production environment.

In an embodiment, the observation part may capture the uncertainty inobserving the true value if the underlying process was known. Theobservation part may be represented as follows:Y _(t)=μ_(t) +v _(t) ,v _(t) ˜N(0,V),

where:

-   -   Y_(t) is a random variable representing the observation,    -   μ_(t) is a mean value of the process at time t,    -   v_(t) is a random error associated with observation uncertainty        at time t, and    -   V is the variance of the random error v_(t).

The system part may be represented as follows:μ_(t) =G _(t)μ_(t-1)+ω_(t) ,w _(t) ˜N(0,W),

where

μ_(t) is a mean value of the forecast,

G_(t) is a constant value,

μ_(t-1) is a mean value of the previous forecast, and

W is a variance associated with μt.

In an embodiment, the model may include historical data associated witha print-related service. For example, the model may be generated usingobserved demand information associated with the print-related serviceover a certain period of time. For instance, a model corresponding to abinding print-related service may incorporate demand informationassociated with print jobs requiring binding over a previous one-yearperiod. Other time periods may be used within the scope of thisdisclosure.

In an embodiment, the demand data associated with a print-relatedservice that has been observed up to time t may be represented asfollows:D _(t) ={Y _(t) ,D _(t-1)}.

In an embodiment, new demand data may be incorporated 105 into a modelfor a print-related service. The new demand data may include observeddemand data over a certain time period. For example, a modelcorresponding to a binding print-related service may include historicaldata through the previous day. When demand data associated with thebinding print-related service is observed for the current day, thatdemand data may be incorporated 105 into the model. In an embodiment,forecasting may be done recursively. Initial values of the mean, m₀, thevariance, C₀, the observation variance, V, and/or the system variance, Wmay be subjectively estimated. As more data is included in the model,the initial values may be less influential on the forecast.

In an embodiment, the incorporation of new demand data into a model maybe represented by the following:

Posterior to observing Y_(t-1): (u_(t-1)|D_(t-1))˜N(m_(t-1), C_(t-1)),

where m_(t-1) is the mean of the print demand process at time t−1, and

C_(t-1) is the variance of the print demand process at time t−1.

In an embodiment, the mean and variance may be updated when a newobservation is available.

Prior to observing Y_(t), the distribution of the mean of the systempart may be represented by: (u_(t)|D_(t-1))˜N(m_(t-1), R_(t)), whereR_(t)=C_(t-1)+W

Distribution of the demand at time t, Y_(t), based on all demandinformation before time t:(Y _(t) |D _(t-1))˜N(f _(t) ,Q _(t)), where f _(t) =m _(t-1) and Q _(t)=C _(t-1) +W+V.

Posterior to observing Y_(t): (u_(t)|D_(t))˜N(m_(t), C_(t)) wherem_(t)=m_(t-1)+A(Y_(t)−f_(t))

${{{where}\mspace{14mu} C_{t}} = {A_{t}V}},{A_{t} = {\frac{R_{t}}{Q_{t}} = \frac{C_{t - 1} + W}{C_{t - 1} + W + V}}},{and}$$C_{t} = {V{\frac{C_{t - 1} + W}{C_{t - 1} + W + V}.}}$

In an embodiment, the forecast for demand at time t may be the estimatedmean of Y_(t): f_(t)=m_(t-1). An estimate of the variance of the demandY_(t) may be represented by Q_(t)=C_(t-1)+W+V, and this varianceestimate may be used to compute a confidence interval around theforecast f_(t)=m_(t-1).

In an embodiment, the model may be updated 110 with interventioninformation. Intervention information may be provided by a user and mayinclude demand information that is outside of the model. In anembodiment, intervention information may include an anticipated demandvalue associated with a time and/or a confidence value associated withthe anticipated demand value. For example, intervention information maybe represented as probability statements, such as “next quarter weexpect demand to be double the historical average, plus or minus 10%.”In this example, the anticipated demand value is an amount equal todouble the historical average, and the confidence value is +/−10%.

In an embodiment, the model associated with the intervention informationmay be updated 110 to account for the intervention information. As such,the model may be updated 110 with principled intervention informationthat is outside of the model to anticipate demand changes.

For example, suppose at time t, a user knows that the mean associatedwith a demand distribution corresponding to a print-related service willincrease by η, and the uncertainty associated with η is represented byvariance ρ². A user may intervene to update the observational error,ω_(t), at time t: (ω_(t)˜N(η, ρ²) and thus:μ_(t) |D _(t-1)=μ_(t-1) |D _(t-1)+ω_(t) |D _(t-1); and(μ_(t) |D _(t-1))˜N(m _(t-1) +η,C _(t-1) +V+ρ ²).

The updated forecast may be represented by:(Y _(t) |D _(t-1))˜N(m _(t-1) +η,C _(t-1) +V _(t)+ρ²).

In an embodiment, the model may be updated with a new mean representedby m_(t-1)+η and a new system variance represented by W_(t)=p².

In an embodiment, a demand forecast associated with a print-relatedfunction may be generated 115 using the updated predictive model. Thedemand forecast may be an estimate of the demand associated with aprint-related service at a certain time. In an embodiment, the demandforecast may also include an error value which may represent theuncertainty associated with the demand forecast.

EXAMPLE 1 Updating a Model

Initial knowledge may be represented as follows:

Observation Equation:Y _(t)=μ_(t) +v _(t) ,v _(t) ˜N(0,100)V=100;

System Equation:μ_(t)=μ_(t-1)+ω_(t),ω_(t) ˜N(0,5)W=5;

Initial Information:(u ₀ |D ₀)˜N(m ₀ ,C ₀)=N(130,400)m ₀=130,C ₀=400

At time t=1:

The system model before observing Y₁ may be represented by thefollowing:(u ₁ |D ₀)˜N(m ₀ ,R ₁);m ₁ =m ₀=130;R=C ₀ +W=400+5=405.

The forecast Y_(1.) before a value of Y₁ is observed, may be representedby the following:f ₁ =m ₀=130, with a variance Q ₁ =C ₀ +W+V=400+5+100=505.

If it is observed that Y₁=150, the model may be updated:

(u₁❘D₁) ∼ N(m₁, C₁)${C_{1} = {{V\left( \frac{C_{0} + W}{C_{0} + W + V} \right)} = {{100\left( \frac{400 + 5}{400 + 5 + 100} \right)} = 80.2}}},{A_{1} = {\left( \frac{C_{0} + W}{C_{0} + W + V} \right) = {\left( \frac{400 + 5}{400 + 5 + 100} \right) = 0.802}}},{m_{1} = {{m_{0} + {A_{1}\left( {Y_{1} - f_{1}} \right)}} = {{130 + {0.802\left( {150 - 130} \right)}} = 146.2}}}$(u₁❘D₁) ∼ N(146.2, 80.2)

At time t=2:

The system model before observing Y₂ may be represented by thefollowing:(u ₂ |D ₁)˜N(m ₁ ,R ₂);m ₁=146.2;R ₂ =C ₁ +W=80.2+5=85.2.

The forecast Y₂, before a value of Y₂ is observed, may be represented bythe following:f ₂ =m ₁=146.2, with a variance Q ₂ =C ₁ +W+V=80.2+5+100=185.2.

If it is observed that Y₂=136, the model may be updated:

(u₂❘D₂) ∼ N(m₂, C₂)${C_{2} = {{V\left( \frac{C_{1} + W}{C_{1} + W + V} \right)} = {{100\left( \frac{80.2 + 5}{80.2 + 5 + 100} \right)} = 46.0}}},{A_{1} = {\left( \frac{C_{1} + W}{C_{1} + W + V} \right) = {\left( \frac{80.2 + 5}{80.2 + 5 + 100} \right) = 0.46}}},{m_{2} = {{m_{1} + {A_{2}\left( {Y_{2} - f_{2}} \right)}} = {{146.2 + {0.46\left( {136 - 146.2} \right)}} = 141.5}}},{\left( {u_{2}❘D_{2}} \right) \sim {{N\left( {141.5,46.0} \right)}.}}$

The model may continue to be updated for any number of observations.Table 1 illustrates an exemplary chart of values associated with a modelbefore and after a value of Y is observed.

TABLE 1 Before Observing Y After Observing Y t Y_(t) m_(t) R_(t) f_(t)Q_(t) m_(t) C_(t) A_(t) 1 150 130.00 405.00 130.00 505.00 146.04 80.200.80 2 136 146.04 85.20 146.04 185.20 141.42 46.00 0.46 3 135 141.4251.00 141.42 151.00 139.25 33.78 0.34 4 114 139.25 38.78 139.25 138.78132.20 27.94 0.28 5 137 132.20 32.94 132.20 132.94 133.39 24.78 0.25 6149 133.39 29.78 133.39 129.78 136.97 22.95 0.23 7 130 136.97 27.95136.97 127.95 135.45 21.84 0.22 8 130 135.45 26.84 135.45 126.84 134.2921.16 0.21 9 123 134.29 26.16 134.29 126.16 131.95 20.74 0.21 10 128131.95 25.74 131.95 125.74 131.14 20.47 0.20 11 128 131.14 25.47 131.14125.47 130.51 20.30 0.20 12 130 130.51 25.30 130.51 125.30 130.40 20.190.20 13 121 130.40 25.19 130.40 125.19 128.51 20.12 0.20 14 114 128.5125.12 128.51 125.12 125.60 20.08 0.20 15 125 125.60 25.08 125.60 125.08125.48 20.05 0.20

EXAMPLE 2 Intervention

Suppose it is known that the demand associated with a print-relatedservice will increase by 200 documents per day from time t=9 to t=10 dueto a new customer. This information may be represented as η=200. Theuncertainty associated with this estimate may be represented by ρ²=300.The new model may intervene at time t=10 by increasing the model mean by200, and the variance by ρ² rather than W. For example, Q_(t)=C_(t-1)+ρ²rather than Q_(t)=C_(t-1)+W. As such, (Y_(t)|D_(t-1))˜N(m_(t-1)+η,C_(t-1)+V+ρ²). The forecast f₁₀ may now equal m₉+200.

For example, using the information in Example 1 and Table 1, at timet=9, (u₉|D₉)˜N (m₉, C₉)=N(134.29, 20.74). Before observing Y₁₀=320, Y₁₀is forecasted as f₁₀=m₉+200=334.29 with varianceQ=(100+20.74+300)=420.74. Table 2 illustrates an exemplary chart ofvalues associated with a model having an intervention at time t=10.

TABLE 2 Before Observing Y After Observing Y t Y_(t) m_(t) R_(t) f_(t)Q_(t) m_(t) C_(t) A_(t) 1 150 130.00 405.00 130.00 505.00 146.04 80.200.80 2 136 146.04 85.20 146.04 185.20 141.42 46.00 0.46 3 135 141.4251.00 141.42 151.00 139.25 33.78 0.34 4 114 139.25 38.78 139.25 138.78132.20 27.94 0.28 5 137 132.20 32.94 132.20 132.94 133.39 24.78 0.25 6149 133.39 29.78 133.39 129.78 136.97 22.95 0.23 7 130 136.97 27.95136.97 127.95 135.45 21.84 0.22 8 130 135.45 26.84 135.45 126.84 134.2921.16 0.21 9 123 134.29 26.16 134.29 126.16 131.95 20.74 0.21 10 320131.95 25.74 334.29 420.74 129.51 20.47 0.20 11 350 129.51 25.47 329.51420.47 133.67 20.30 0.20 12 310 133.67 25.30 333.67 420.30 128.89 20.190.20 13 330 128.89 25.19 328.89 420.19 129.11 20.12 0.20 14 305 129.1125.12 329.11 420.12 124.27 20.08 0.20 15 345 124.27 25.08 324.27 420.08128.43 20.05 0.20

FIG. 2 illustrates an exemplary graph of Y_(t) 210, the time series withintervention 205 and the time series without intervention 200. Asillustrated by FIG. 2, the model requires a significant amount of timeto adjust without the use of intervention.

In an embodiment, the demand forecast may be displayed 120 to a user ona graphical user interface. For example, the demand forecast may bedisplayed 120 to a user on a computer, a mobile computing device, aprint production resource and/or the like. The demand forecast may bedisplayed 120 as a graphical representation, a chart representationand/or the like.

In an embodiment, an amount of inventory associated with a print-relatedfunction may be assessed 125 using the generated demand forecast. Forexample, a current inventory level may be compared to an inventory levelnecessary to supply the demand forecast. If the currently inventorylevel does not exceed the inventory level necessary to supply the demandforecast, additional inventory may be ordered.

FIG. 3 depicts a block diagram of exemplary internal hardware that maybe used to contain or implement program instructions according to anembodiment. A bus 300 serves as the main information highwayinterconnecting the other illustrated components of the hardware. CPU305 is the central processing unit of the system, performingcalculations and logic operations required to execute a program. Readonly memory (ROM) 310 and random access memory (RAM) 315 constituteexemplary memory devices.

A controller 320 interfaces with one or more optional memory devices 325to the system bus 300. These memory devices 325 may include, forexample, an external or internal DVD drive, a CD ROM drive, a harddrive, flash memory, a USB drive or the like. As indicated previously,these various drives and controllers are optional devices.

Program instructions may be stored in the ROM 310 and/or the RAM 315.Optionally, program instructions may be stored on a tangible computerreadable medium such as a compact disk, a digital disk, flash memory, amemory card, a USB drive, an optical disc storage medium, such asBlu-ray™ disc, and/or other recording medium.

An optional display interface 330 may permit information from the bus300 to be displayed on the display 335 in audio, visual, graphic oralphanumeric format. Communication with external devices may occur usingvarious communication ports 340. An exemplary communication port 340 maybe attached to a communications network, such as the Internet or anintranet.

The hardware may also include an interface 345 which allows for receiptof data from input devices such as a keyboard 350 or other input device355 such as a mouse, a joystick, a touch screen, a remote control, apointing device, a video input device and/or an audio input device.

An embedded system, such as a sub-system within a xerographic apparatus,may optionally be used to perform one, some or all of the operationsdescribed herein. Likewise, a multiprocessor system may optionally beused to perform one, some or all of the operations described herein.

It will be appreciated that various of the above-disclosed and otherfeatures and functions, or alternatives thereof, may be desirablycombined into many other different systems or applications. Also thatvarious presently unforeseen or unanticipated alternatives,modifications, variations or improvements therein may be subsequentlymade by those skilled in the art which are also intended to beencompassed by the following claims.

What is claimed is:
 1. An inventory management system for forecastingdemand in a print production environment, the system comprising: acomputing device; and a computer-readable storage medium incommunication with the computing device, the computer-readable storagemedium comprising one or more programming instructions for: updating apredictive model, by a computing device, with intervention informationthat is outside of the predictive model, wherein the interventioninformation comprises an anticipated demand value and a confidence valueassociated with the anticipated demand value, wherein the predictivemodel is associated with a demand distribution of a print-relatedservice in a print production environment, incorporating new demand datainto the predictive model associated with the print-related service,wherein the new demand data comprises an observed demand valueassociated with a time period, wherein the one or more programminginstructions for incorporating new demand data into the predictive modelcomprise one or more programming instructions for: identifying a meanvalue associated with the demand distribution, determining an errorvalue equal to a difference between the observed demand value and aprevious forecast value associated with the print-related service,determining a weighted error value by multiplying the error value by aweight value, and identifying a new mean value associated with thedemand distribution by summing the mean value and the weighted errorvalue, generating a demand forecast associated with the print-relatedservice by using the updated predictive model, using the generateddemand forecast to compare a current inventory level associated with theprint-related service to an anticipated inventory level associated withthe demand forecast of the print-related service, and orderingadditional inventory in response to the current inventory level beingless than the anticipated inventory level.
 2. The system of claim 1,wherein the one or more programming instructions for updating apredictive model comprise one or more programming instructions for:identifying a predictive model that incorporates historical demand dataassociated with the print-related service.
 3. The system of claim 2,wherein the one or more programming instructions for identifying apredictive model comprise one or more programming instructions forgenerating the predictive model using historical data received from oneor more print devices that offer the print-related service.
 4. Thesystem of claim 2, wherein the one or more programming instructions foridentifying a predictive model comprise one or more programminginstructions for generating the predictive model using historical datareceived from a user.
 5. The system of claim 2, wherein the one or moreprogramming instructions for identifying a predictive model comprise oneor more programming instructions for identifying a Bayesian time seriesmodel.
 6. The system of claim 1, wherein the one or more programminginstructions for updating the predictive model with interventioninformation comprise one or more programming instructions for:receiving, from a user, the anticipated demand value and the confidencevalue, wherein the anticipated demand value for the print-relatedservice represents a demand at one or more times, wherein the confidencevalue represents a probability that the anticipated demand value iswithin a range; and incorporating the received anticipated demand valueand the received confidence value into the predictive model.
 7. Thesystem of claim 1, wherein the one or more programming instructions forupdating the predictive model with intervention information comprise oneor more programming instructions for: updating the predictive model withintervention information represented by a probability statementcomprising the anticipated demand value and the confidence value.
 8. Thesystem of claim 1, further comprising one or more programminginstructions for: displaying, via the computing device, the generateddemand forecast.
 9. The system of claim 1, further comprising: a printproduction resource configured to perform the print-related service,wherein the one or more programming instructions further comprise one ormore programming instructions for displaying, via the print productionresource, the generated demand forecast.
 10. A method of forecastingdemand in a print production environment, the method comprising:updating a predictive model, by a computing device, with interventioninformation that is outside of the predictive model, wherein theintervention information comprises an anticipated demand value and aconfidence value associated with the anticipated demand value, whereinthe predictive model is associated with a demand distribution of aprint-related service in a print production environment; incorporating,by a computing device, new demand data into the predictive modelassociated with the print-related service, wherein the new demand datacomprises an observed demand value associated with a time period,wherein incorporating new demand data into the predictive modelcomprises: identifying a mean value associated with the demanddistribution, determining an error value equal to a difference betweenthe observed demand value and a previous forecast value associated withthe print-related service, determining a weighted error value bymultiplying the error value by a weight value, and identifying a newmean value associated with the demand distribution by summing the meanvalue and the weighted error value, generating a demand forecastassociated with the print-related service by using the updatedpredictive model; using the generated demand forecast to compare acurrent inventory level associated with the print-related service to ananticipated inventory level associated with the demand forecast of theprint-related service; and ordering additional inventory in response tothe current inventory level being less than the anticipated inventorylevel.
 11. The method of claim 10, wherein updating a predictive modelcomprises: identifying a predictive model that incorporates historicaldemand data associated with the print-related service.
 12. The method ofclaim 11, wherein the identifying a predictive model comprisesgenerating a predictive model using historical data received from one ormore print devices that offer the print-related service.
 13. The methodof claim 11, wherein identifying a predictive model comprises generatinga predictive model using historical data received from a user.
 14. Themethod of claim 11, wherein identifying a predictive model comprisesidentifying a Bayesian time series model.
 15. The method of claim 10,wherein updating the predictive model with intervention informationcomprises: receiving, from a user, the anticipated demand value and theconfidence value, wherein the anticipated demand value for theprint-related service represents a demand at one or more times, whereinthe confidence value represents a probability that the anticipateddemand value is within a range; and incorporating the receivedanticipated demand value and the received confidence value into thepredictive model.
 16. The method of claim 10, wherein updating thepredictive model with intervention information comprises: updating thepredictive model with intervention information represented by aprobability statement comprising the anticipated demand value and theconfidence value.
 17. The method of claim 10, further comprising:displaying, via the computing device, the generated demand forecast. 18.The method of claim 10, further comprising: displaying, via a printproduction resource, the generated demand forecast.